the diagram represents three statements about teachers: p, q, and r. for how many teachers are both p ∧ r…
the diagram represents three statements about teachers: p, q, and r. for how many teachers are both p ∧ r true and q false? 2 4 5 9
Answer
Explanation:
Step1: Understand logical - AND operation
We want to find where $p\land r$ is true and $q$ is false. The symbol $\land$ means logical - AND, so $p\land r$ is true when both $p$ and $r$ are true.
Step2: Analyze Venn - diagram regions
In a Venn - diagram, the region where $p$ and $r$ are true is the intersection of circles $p$ and $r$. The intersection of $p$ and $r$ consists of two sub - regions: one that is also part of $q$ (the triple - intersection $p\cap q\cap r$) and one that is not part of $q$. The triple - intersection $p\cap q\cap r$ has 2 elements, and the intersection of $p$ and $r$ that is not part of $q$ has 9 elements. We want the part of $p\cap r$ where $q$ is false.
Step3: Identify the correct region
The region where $p\land r$ is true and $q$ is false is the part of the intersection of $p$ and $r$ that is outside of $q$. Looking at the Venn - diagram, the number of elements in the intersection of $p$ and $r$ that are not in $q$ is 9.
Answer:
9